Probabilistic Interpretation of Solutions of Linear Ultraparabolic Equations

Abstract

We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.

Keywords

• ultraparabolic equation
• ultradiffusion process
• probabilistic representation
• mathematical finance